Post-Lie algebras of derivations and regularity structures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914278403997696 |
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| author | Jacques, Jean-David Zambotti, Lorenzo |
| author_facet | Jacques, Jean-David Zambotti, Lorenzo |
| contents | Given a commutative algebra $\mathcal{A}$, we exhibit a canonical structure of post-Lie algebra on the space $\mathcal{A}\otimes {\rm Der}(\mathcal{A})$ where ${\rm Der}(\mathcal{A})$ is the space of derivations on $\mathcal{A}$, in order to use the machinery given by Oudom-Guin (2008) and Ebrahimi-Fard--Lundervold--Munthe-Kaas (2015), and to define a Hopf algebra structure on the associated enveloping algebra with a natural action on $\mathcal{A}$. We apply these results to the setting of Linares-Otto-Tempelmayr (2023), giving a simpler and more efficient construction of their action and extending the recent work by Bruned-Katsetsiadis (2023). This approach gives an optimal setting to perform explicit computations in the associated structure group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Post-Lie algebras of derivations and regularity structures Jacques, Jean-David Zambotti, Lorenzo Mathematical Physics Analysis of PDEs Probability Rings and Algebras 16S30, 16T05, 60L30, 60L70 Given a commutative algebra $\mathcal{A}$, we exhibit a canonical structure of post-Lie algebra on the space $\mathcal{A}\otimes {\rm Der}(\mathcal{A})$ where ${\rm Der}(\mathcal{A})$ is the space of derivations on $\mathcal{A}$, in order to use the machinery given by Oudom-Guin (2008) and Ebrahimi-Fard--Lundervold--Munthe-Kaas (2015), and to define a Hopf algebra structure on the associated enveloping algebra with a natural action on $\mathcal{A}$. We apply these results to the setting of Linares-Otto-Tempelmayr (2023), giving a simpler and more efficient construction of their action and extending the recent work by Bruned-Katsetsiadis (2023). This approach gives an optimal setting to perform explicit computations in the associated structure group. |
| title | Post-Lie algebras of derivations and regularity structures |
| topic | Mathematical Physics Analysis of PDEs Probability Rings and Algebras 16S30, 16T05, 60L30, 60L70 |
| url | https://arxiv.org/abs/2306.02484 |